Is there a way to fill in hollow objects?
If i understand you, you have the airways components as one object and a cube that you placed around it.

If so, then i would believe all you need to do is the following:


Select the airway components and go in edit mode
Press A to select all elements
Press Alt+N and select "Flip" to flip the normals. (the outsides become the insides and vice versa)
Now go back in object mode and select the cube/block and the airways components
Press Ctrl+J and you will have an object that considers the empty area the inside of the airways components as outside while the area between the outside of the cube/block and the airways components are considered inside and will be filled.
There might be small parts that you will have to adjust, depending on where and how many outlets/openings you need for the airways components. That part should be easy to deal with if you loop cut or inset faces to generate enough vertices to connect the airways components outlets to the outside of the cube. Using "X-Ray" Alt+Z it should look something like this "very" simplified version.

To finish it, make sure to check the "Face Orientation" once more.

The outside of the cube/block should be blue and the connections from outside to the hollow airways components needs to be blue inside of their hollow parts, while if you go through the cube/block with the camera, it should show all red as you would move through the area considered inside the object where the 3D software (slicer) would give you the options to fill.



It's important to make sure that no surface has red and blue colored faces on the same side! But the "Solid" check of the "3D-Print Toolbox" add-on  will test for that.

Happy Blending.